Problem: Simplify the following expression: $r = \dfrac{2}{8y - 3} \div \dfrac{4}{6y}$
Answer: Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{2}{8y - 3} \times \dfrac{6y}{4}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 2 \times 6y } { (8y - 3) \times 4}$ $r = \dfrac{12y}{32y - 12}$ Simplify: $r = \dfrac{3y}{8y - 3}$